(n.) a troublesome issue, an unwelcome or harmful matter requiring a solution
When you have a problem, etymologically you have something that needs to be ‘thrown forward’ for discussion or solution. That’s because the word problem pulls together the Greek roots pro (meaning ‘forward’) and ballein (meaning ‘to throw’, or ‘to project’).
In the sense of a problem being ‘put forward’ in order to be solved, the first problems were probably disputatious issues, moral quandaries, logical and philosophical puzzles, and other similarly enigmatic questions and issues put forward for active collaborative debate back in the days of Ancient Greece. (Hence the title of Aristotle’s Problems, an anthology of debatable issues likely written and expanded on by him and his followers in the second–fifth centuries AD.)
That being said, the more general and more usual use of the word problem to describe a tricky and unwelcome issue or stumbling block, was also in use back in Greek—suggesting that for as long as thinkers and scientific minds have been imagining problems requiring deep debate and thought, life has been presenting people with no less troublesome matters too.
As we mentioned over on Twitter, though, through its etymology problem has some intriguing historical cousins. That verb ballein, ‘to throw’, is also the root of ballistics, the science of projectiles. It’s also found in a person’s metabolism (the process that literally ‘throws someone into a state of change’), a hyperbolic comparison (literally one thrown ‘too far’), anabolic steroids (from Greek roots meaning ‘thrown (i.e. built) up’), a geometric hyperbola (a curve ‘thrown beyond’), and even—according to popular theories, at least—Spain’s Balearic Islands, so named because of their inhabitants’ expert use of slings and other throwing weapons.